In a medium mixing bowl, combine olive oil, lime juice, minced garlic, chili powder, cumin, salt, black pepper, and cayenne pepper. Whisk until well mixed.
Place the chicken breasts in a large resealable bag or shallow dish and pour the marinade over the chicken. Seal the bag or cover the dish and marinate in the refrigerator for at least 30 minutes or up to 2 hours.
Preheat the grill or grill pan to medium-high heat.
Remove the chicken from the marinade and discard the marinade. Grill the chicken for 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C).
While the chicken is grilling, prepare the avocado salsa. In a mixing bowl, combine diced avocados, cherry tomatoes, red onion, cilantro, and lime juice. Season with salt and pepper to taste and gently toss to combine.
Once the chicken is cooked, remove it from the grill and let it rest for a few minutes before slicing.
Serve the grilled chicken topped with a generous amount of avocado salsa.